A flight plan is made up of a set of flight path segments of different types. These different types of segments are, for example, defined in the Arinc 424 standard. In the case of this standard, the segments are as follows:                The IF (Initial Fix) segment, which is defined by a fixed initial point on the ground.        The CF (Course To a Fix) segment, which is defined by a trajectory joining then following a route on the ground to reach a fixed point.        The DF (Direct to a fix) segment, which is defined by a trajectory to a fixed point. This trajectory is not necessarily straight, in fact the aircraft seeks in this type of segment to reach the point of arrival without necessarily following a straight line. Thus, in the event an offset induced, for example, by a maneuver or by a cross wind, this offset is not compensated.        The TF (Track between two fixes) segment, which is defined by a great circle route between two fixed points. A great circle route designates the shortest path between two points of a sphere, that is to say the great circle arc which passes through these two points. The difference between a segment of DF type and a TF segment is represented in FIG. 1.        The AF (Arc DME to a Fix) segment, which is defined by a circular arc of determined radius whose center is a beacon or radio transmitter of “DME” (Distance Measuring Equipment) type.        The RF (Radius to a Fix) segment, which is defined by a circular arc, of determined center and radius. This circular arc is in addition implemented between two fixed points. The description of this segment also includes a direction of travel to determine which of the two possible circular arcs must be chosen.        The VI (Heading to intercept) segment, which is defined by a heading to be followed to the intersection with the next segment. The heading is the angle between North (geographic or magnetic) and the fuselage of the airplane. In practice, the heading is given by a compass present in the aircraft. Air related legislation, such as the United States Federal Aviation Regulations (FARs), demands the presence of a compass in an aircraft.        The CI (Course to Intercept) segment, which is defined by a route to be followed to the intersection with the next segment. The route is the angle between North (geographic or magnetic) and the speed vector of the airplane. Determining the route means having to know the movement of the airplane relative to the ground. In practice, this implies the presence of a satellite positioning system, for example equipment of GPS (Global Positioning System) type or equipment of Galileo type, or the presence of a system of inertial type, in the aircraft. Air legislation does not demand the presence of a satellite positioning system or of a system of inertial type in an aircraft, which is why the flight plans are described mainly by using segments defined by a heading rather than segments defined by a route, to be compatible with the older aircraft or aircraft not equipped with a satellite positioning system or a system of inertial type.        The VA (Heading to Altitude) segment which is defined by a heading to be followed to a given altitude.        The CA (Course to Altitude) segment, which is defined by a route to be followed to a given altitude.        The FA (Fix to Altitude) segment, which is defined by a route to be followed, starting from a fixed point and to a given altitude.        The VD (Heading to DME Distance) segment, which is defined by a heading to be followed to the intersection with a circular arc whose center is a beacon or a radio transmitter of “DME” type.        The CD (Course to DME Distance) segment, which is defined by a route to be followed to the intersection with a circular arc whose center is a beacon or a radio transmitter of “DME” type.        The VR (Heading to Radial) segment, which is defined by a heading to be followed to the intersection with a specified radial (a radial corresponds to a straight line starting from a point and forming a determined angle with geographic North).        The CR (Course to Radial) segment, which is defined by a route to be followed to the intersection with a specified radial (a radial corresponds to a straight line starting from a point and forming a determined angle with geographic North).        The FC (Track from Fix to Distance) segment, which is defined by a route starting from a point that is explicitly defined, in a database, by its coordinates of latitude/longitude/altitude type and having a specific duration.        The FD (Track from Fix to DME Distance) segment, which is defined by a route starting from a point that is explicitly defined, in a database, by its coordinates of latitude/longitude/altitude type and finishing at the intersection with a circular arc whose center is a beacon or a radio transmitter of “DME” type.        The VM (Heading to Manual) segment, which is defined by a heading. The end of this segment is determined by the pilot and it is not therefore known in advance.        The FM (Fix to Manual) segment, which is defined by a route starting from a point that is explicitly defined, in a database, by its coordinates of latitude/longitude/altitude type. The end of this segment is determined by the pilot and it is not therefore known in advance.        The HA segment, which is defined by a portion of circuit in the form of a race-track pattern, the end of which depends on the altitude.        The HF segment, which is defined by a circuit in the form of a race-track pattern implemented during a single turn.        The HM segment, which is defined by a circuit in the form of a race-track pattern with no exit condition, upon manual activation.        The PI (Procedure Intercept) segment, which is defined by a route moving away from a fixed point then a half-turn and finally a route having an intersection with the next segment. Note that the Arinc 424 standard allows this type of segment to be followed only by segments of CF type. These segments of CF type have the characteristics of having a final point corresponding to the initial point of the segment of PI type and of having a route corresponding to the opposite of the route of the segment of PI type.        
When transcribing the flight plan into a trajectory, it is necessary to take account of all of the transitions of the flight plan. A transition is a trajectory element that links two segments together in a flyable manner. Now, the algorithm for determining the trajectory of the airplane during a transition depends on the type of the two segments of the transition. In the case of the Arinc 424 standard, this standard has 23 different segment types. There are therefore potentially 529 transition combinations, and consequently 529 different algorithms. In practice, the Arinc 424 standard defines a certain number of restrictions and interdictions in the transitions between segments, which makes it possible to reduce the number of combinations. Nevertheless, for operational needs, some cases prohibited by the Arinc 424 standard sometimes have to be implemented by the FMS because they correspond to a real need of the crew. Furthermore, the data present in the databases are not always perfect and many particular cases can occur and require specific management. The implementation of all these algorithms means that the flight plan transcription system is highly complex. This high complexity notably has impacts during the flight plan transcription system validation process. In practice, because of the large number of algorithms implemented, the tests carried out during the validation process cannot be exhaustive and therefore risk not reflecting all the transition conditions. The system obtained as described above therefore risks not being reliable and provoking failures that can be critical.
Furthermore, in the case of changes to the Arinc 424 standard, or to adapt the transcription of the flight plan to the inclusion of a new standard, it is necessary to modify all of the flight plan transcription algorithms. In particular, it is necessary to modify the algorithms that make it possible to determine the trajectory of the aeroplane during the transitions. This complexity results in a significant financial cost for the development of the modifications of the algorithm.